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# Multidimensional Case
from scipy.stats import random_correlation

seed = 2222                       

dim = 10

T = 1
N = int(2.**9)
S0 = np.random.normal(100, 1, dim)

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# Two-dimensional Case

seed = 22                       

dim = 2; T = 1; N = int(2.**9)

S0 = np.array([100, 100])

# Parameter Estimation

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#Visualize the closing price history
import matplotlib.pyplot as plt

plt.figure(figsize = (16,8))
plt.title('Close Price History', fontsize = 18)
plt.plot(intc['Adj Close'])
plt.plot(amd['Adj Close'])
plt.legend(['INTC', 'AMD'], loc = 'upper left', fontsize = 18)
plt.xlabel('Date', fontsize = 18)
plt.ylabel('Close Price USD ($)', fontsize = 18)

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import pandas_datareader as pdr
from datetime import datetime

intc = pdr.get_data_yahoo(symbols='INTC', start=datetime(2018, 1, 1), end=datetime(2020, 1, 1))
amd = pdr.get_data_yahoo(symbols='AMD', start=datetime(2018, 1, 1), end=datetime(2020, 1, 1))

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# Asset Path
import numpy as np

def GBMsimulator(seed, So, mu, sigma, Cov, T, N):
    """
    Parameters

    seed:   seed of simulation
    So:     initial stocks' price
    mu:     expected return